CONSTRUCTIVE SYMBOLIC PRESENTATIONS OF RANK ONE MEASURE-PRESERVING SYSTEMS

Terrence Adams , Sébastien Ferenczi (1) , Karl Petersen (2)

1 I2M - Institut de Mathématiques de Marseille
2 Department of Mathematics [Chapel Hill]

Given a rank one measure-preserving system defined by cutting and stacking with spacers, we produce a rank one binary sequence such that its orbit closure under the shift transformation, with its unique nonatomic invariant probability, is isomorphic to the given system. In particular, the classical dyadic odometer is presented in terms of a recursive sequence of blocks on the two-symbol alphabet {0, 1}. The construction is accomplished using a definition of rank one in the setting of adic, or Bratteli-Vershik, systems.

Domaines: Mathématiques [math]

Terrence Adams, Sébastien Ferenczi, Karl Petersen. CONSTRUCTIVE SYMBOLIC PRESENTATIONS OF RANK ONE MEASURE-PRESERVING SYSTEMS. Colloquium Mathematicum, 2017, 150, pp.243-255. ⟨hal-02120135⟩